How do you find the instantaneous rate of change of the function $f(x)= ln (2x)$ when x=3?

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Answer 1 · 2016-04-08T20:01:08

$1/3$

Instantaneous rate of change just means the derivative or gradient at a point.

To differentiate the function, we do

$f(x) = ln2x = ln2 + lnx$

and, because $ln2$ is just a constant and has a derivative of $0$ ,

$f(x) = lnx$
$f'(x) = 1/x$

Now, when $x = 3$ ,

$1/x = 1/3$

How do you find the instantaneous rate of change of the function f(x)= ln (2x) f(x)= ln (2x) when x=3?